y^'-y=4sin(3t)

Lösung

y^{^{'}} - y = 4 sin (3 t)

y = \frac{2 e ^{t} ( - 3 e ^{- t} cos ( 3 t ) - e ^{- t} sin ( 3 t ) )}{5} + c_{1} e^{t}

Schritte zur Lösung

y^{'} (t) - y = 4 sin (3 t)

Solve linear ODE:

y = \frac{2 e ^{t} ( - 3 e ^{- t} cos ( 3 t ) - e ^{- t} sin ( 3 t ) )}{5} + c_{1} e^{t}

y = \frac{2 e ^{t} ( - 3 e ^{- t} cos ( 3 t ) - e ^{- t} sin ( 3 t ) )}{5} + c_{1} e^{t}

in v erse l a pl a ce \frac{1}{s - 1}

n = 4 \sum \infty \frac{1}{( n ) ( n + 1 )}

\int_{0}^{x} \frac{1}{( 1 - x )} d x

x \to 0 lim (\frac{1}{1 - e ^{x}})

n = 1 \sum \infty (cos (32))^{n}